Testing constraints on periodic quantum evolution as a probe of incoherent error using a trapped-ion quantum computer

As quantum computers and simulators begin to produce results which cannot be verified classically, it will become imperative to develop effective tools to diagnose experimental errors on these devices. While state or process tomography is a natural way to probe sources of experimental error, the intense measurement requirements make these strategies infeasible in all but the smallest of quantum systems. In this talk, I will discuss the ways in which long-term dynamics under periodic driving can act as a sensitive, low-cost probe of incoherent error. I will present a measurement scheme built on easily accessible observables measured at varying times in the evolution. These measurements are constrained by theoretical bounds that become exponentially tight with evolution time, providing progressively stronger checks for the presence of incoherent error. I will include results from experimental implementation of this scheme in the presence of varying levels of incoherent error on two quantum computers, including our own trapped-ion experiment, and demonstrate the conditions under which deviations of the formulated bounds constitute a practical detection of incoherent error.